Solve the following quadratic equation: 12abx^2 - (9a^2 - 8b^2)x … - Vidyadip

Question

Solve the following quadratic equation: $12abx^2 - (9a^2 - 8b^2)x - 6ab = 0$

✓

Answer

$12abx^2 - (9a^2 - 8b^2)x - 6ab = 0$
$\Rightarrow 12abx^2 - 9a^2x + 8b^2x - 6ab = 0$
$\Rightarrow 3ax(4bx - 3a) + 2b(4bx - 3a) = 0$
$\Rightarrow (4bx - 3a)(3ax + 2b) = 0$
$\Rightarrow (4bx - 3a) = 0$ or $(3ax + 2b) = 0$
$\Rightarrow 4bx = 3a$ or $3ax = -2b$
$\Rightarrow\text{x}=\frac{\text{3a}}{\text{4b}}$ or $\text{x}=\frac{-\text{2b}^2}{\text{3a}}$
Hence, $\frac{\text{3a}}{\text{4b}}$ and $\frac{-\text{2b}}{\text{3a}}$ are the roots of the given equation.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Question" from Quadratic Equations→Quadratic Equations — all question types→Maths STD 10 question papers→Maharashtra Board STD 10 question papers→Maharashtra Board question paper generator→

Similar questions

Construct a $\triangle\text{ABC},$ in which BC = 5cm, $\angle\text{C}=60^\circ$ and altitude from A is equal to 3cm. Construct a $\triangle\text{ADE}$ similar to $\triangle\text{ABC},$ such that each side of $\triangle\text{ADE}$ is $\frac32$ times the corresponding side of $\triangle\text{ABC}$ Write the steps of construction.

If $\cos\theta+\sin\theta)=\sqrt{2}\sin\theta,$ show that $\sin\theta-\cos\theta=\sqrt{2}\cos\theta.$

Find the mode, median and mean for the following data:

Marks obtained	25-35	35-45	45-55	55-65	65-75	75-85
Number of students	7	31	33	17	11	1

Find the median of the following data by making a 'less than ogive'.

Marks	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90	90-100
Number of students	5	3	4	3	3	4	7	9	7	8

A child puts one five-rupee coin of her saving in the piggy bank on the first day. She increases her saving by one five-rupee coin daily. If the piggy bank can hold 190 coins of five rupees in all, find the number of days she can contribute to put the five-rupee coins onto it and find the tatal money the saved.

Solve the following quadratic equation:$4x^2 - 2(a^2 + b^2)x + a^2b^2 = 0$

If $\angle\text{A}$ and $\angle\text{B}$ are acute angles such that $\sin\text{A}=\sin\text{B}$ then prove that $\angle\text{A}=\angle\text{B}.$

Solve each of the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the x-axis:
x - 2y + 2 = 0, 2x + y - 6 = 0

Prove that $\big(2\sqrt3-1\big)$ is an irrational number.

A man arranges to pay off a debt of $₹ 36000$ by $40$ monthly instalments which form an arithmetic series. When $30$ of the instalments are paid, he dies leaving one-third of the debt unpaid. Find the value of the first instalment.